Special properties, closures and interiors of crisp and fuzzy relations. (English) Zbl 0664.04001
This paper offers optimal definitions of the special properties which relations on a set may possess, and which combine to define the classically important types of preorders, both kinds of orders, tolerances and equivalences. The useful concept of local properties is introduced. The concepts of closure and interior of a relation with respect to a property are defined. Finally, fast algorithms are given for the computer calculation of the more troublesome closures, and a standardized procedure for the analysis of local orders is presented.
Reviewer: Li Sang Ho
MSC:
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
| 03-04 | Software, source code, etc. for problems pertaining to mathematical logic and foundations |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
similarity; relations; preorders; tolerances; equivalences; local properties; closure; interior; fast algorithms; local ordersReferences:
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